Discrete time signals Dag T. Wisland Spring 2014 Outline Impulse - PowerPoint PPT Presentation

INF4420 Discrete time signals Dag T. Wisland Spring 2014

Outline • Impulse sampling • z ‐ Transform • Frequency response • Stability Spring 2014 Discrete time signals 2

Introduction • More practical to do processing on sampled signals in many cases • Sampled + quantized signals = digital • Inputs and outputs are not sampled • How does sampling affect the signals? • Tools for analyzing sampled signals and systems (“discrete Laplace transform”, the z ‐ transform) Spring 2014 Discrete time signals 3

Introduction • We have already seen sample and hold circuits • We can also realize integrators, filters, etc. as sampled analog systems—switched capacitor techniques. Discrete time, continuous amplitude. • Digital processing is efficient and robust, usually preferred where applicable. Sampling also applies to digital. Spring 2014 Discrete time signals 4

Introduction Spring 2014 Discrete time signals 5

Introduction • Sample a continuous time input signal at uniformely spaced time points. • Output is a discrete sequence of values (in theory). Spring 2014 Discrete time signals 6

Introduction Spring 2014 Discrete time signals 7

Sampling Laplace transform: Input signal Fourier transform: Spring 2014 Discrete time signals 8

Sampling Spring 2014 Discrete time signals 9

Sampling Spring 2014 Discrete time signals 10

Sampling Spring 2014 Discrete time signals 11

Sampling Spring 2014 Discrete time signals 12

Sampling Spring 2014 Discrete time signals 13

Sampling Spring 2014 Discrete time signals 14

Sampling Spring 2014 Discrete time signals 15

Spring 2014 Discrete time signals 16

Spring 2014 Discrete time signals 17

Frequency response Spring 2014 Discrete time signals 18

Frequency response Spring 2014 Discrete time signals 19

Frequency response Spring 2014 Discrete time signals 20

Frequency response Spring 2014 Discrete time signals 21

Frequency response Spring 2014 Discrete time signals 22

Frequency response Spring 2014 Discrete time signals 23

Sampling rate conversion • Changing the sampling rate after sampling • We come back to this when discussing oversampled converters • Oversampling = sampling faster than the Nyquist frequency would indicate • Upsampling is increasing the sampling rate (number of samples per unit of time) • Downsampling is decreasing the sampling rate Spring 2014 Discrete time signals 24

Downsampling Keep every n ‐ th sample. Downsample too much: Aliasing Spring 2014 Discrete time signals 25

Upsampling Insert n zero valued samples between each original sample, and low ‐ pass filter. Requires gain to maintain the signal level. Spring 2014 Discrete time signals 26

Discrete time filters Spring 2014 Discrete time signals 27

Discrete time filters Spring 2014 Discrete time signals 28

Stability Spring 2014 Discrete time signals 29

IIR filters Spring 2014 Discrete time signals 30

FIR filters Spring 2014 Discrete time signals 31

Bilinear transform Spring 2014 Discrete time signals 32

Sample and hold Spring 2014 Discrete time signals 33

Sample and hold Spring 2014 Discrete time signals 34

Sample and hold Spring 2014 Discrete time signals 35

Sample and hold Sampled signal spectrum Spring 2014 Discrete time signals 36

References Gregorian and Temes, Analog MOS Integrated Circuits for Signal Processing , Wiley, 1986 Spring 2014 Discrete time signals 37